Average Error: 51.6 → 0.2
Time: 31.7s
Precision: 64
Internal Precision: 1856
\[\sqrt{x - y} - \sqrt{x + y}\]
\[\frac{-\left(y + y\right)}{\sqrt{x - y} + \sqrt{x + y}}\]

Error

Bits error versus x

Bits error versus y

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Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 51.6

    \[\sqrt{x - y} - \sqrt{x + y}\]
  2. Using strategy rm
  3. Applied flip--51.6

    \[\leadsto \color{blue}{\frac{\sqrt{x - y} \cdot \sqrt{x - y} - \sqrt{x + y} \cdot \sqrt{x + y}}{\sqrt{x - y} + \sqrt{x + y}}}\]
  4. Applied simplify0.2

    \[\leadsto \frac{\color{blue}{-\left(y + y\right)}}{\sqrt{x - y} + \sqrt{x + y}}\]

Runtime

Time bar (total: 31.7s)Debug log

herbie shell --seed '#(2775764126 3555076145 3898259844 1891440260 2599947619 1948460636)' 
(FPCore (x y)
  :name "sqrt(x-y)-sqrt(x+y)"
  (- (sqrt (- x y)) (sqrt (+ x y))))